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First, the open loop transfer function is entered. The numerator, n, and the denominator,d, are entered as Matlab vectors representing the coefficients of s in descending powersof s. The transfer function is defined using the function tf. EDU>n=[1];EDU>d=[1 4 0];EDU>g=tf(n,d) Root locus design using Matlab
Transfer function:---------s^2 + 4 s An alternative way of looking at the transfer function is to show it in factored form usingthe zpk (zero-pole-gain) function. EDU>zpk(g)Zero/pole/gain: 1
-------s (s+4) The root locus is plotted using the function rlocus. The root locus plot will be produced.^1
EDU>rlocus(g)
Real Axis
In order to look at just the upper left quadrant of the plot, again use the axis command toset the minimum x value, maximum x value, minimum y value, and maximum y value forthe axes. EDU>axis([-5 1 -1 5])
-1^012 -5 -4 -3 -2 -1 0 1
Real Axis
To put on a grid for the axes marks, use the command grid. EDU>grid
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Real Axis
To find the gain and the values of the roots at a specific point use the command rlocfind.The roots are given as the 'selected point' and the gain is given as' ans=' EDU>rlocfind(g)Select a point in the graphics windowselected_point =ans =-2.0096+ 2.0096i
-1^01 -5 -4 -3 -2 -1 0 1
Real Axis
To check the closed loop response, the closed loop transfer function is found using thecommand, feedback.argument is the feedback path.EDU>CLTF=feedback(g8,1)Transfer function: 8 The first argument is the forward path (Gk) and the second -------------s^2 + 4 s + 8To plot the step response of the system, use the command step on the CLOSED looptransfer function.transfer function.EDU>step(CLTF) A common mistake is to find the step response of the open loop
Time (sec.)
Step Response 0.20.40.6 (^00) 0.5 1 1.5 2 2.5 3
0.81.21.4^1
